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If x=(2t)/(1+t^2),y=(1-t^2)/(1+t^2),then...

If `x=(2t)/(1+t^2)`,`y=(1-t^2)/(1+t^2)`,`then ` find ` (dy)/(dx)`.

Text Solution

Verified by Experts

The correct Answer is:
`(4)/(3)`
`(dx)/(dt)=((1+t^(2))2-2txx2t)/((1+t^(2))^(2))=(2-2t^(2))/((1+t^(2))^(2))`
`(dy)/(dt)((1+t^(2))(-2t)-(1-t^(2))2t)/((1+t^(2))^(2))=(-4t)/((1+t^(2))^(2))`
`therefore" "(dy)/(dx)=(dy//dt)/(dx//dt)=(-4t)/(2-2t^(2))=(2t)/((1+t^(2))^(2))`
`"or "(dy)/(dx):|_(t=2)=(4)/(3)`
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